Chop the potatoes into small pieces, then add to a pot with the eggs. Add enough water to the pot to cover them, cook over medium heat (not so high it boils over) and cook for 14 minutes.
Drain the potatoes, then run under cold water to bring the heat off of them.
Once the items are cooled, peel the eggs and dice, reserving the yolks.
In a bowl mix together the mayonnaise, mustard, sugar, and white vinegar.
Add the cooked egg yolks to the mayonnaise mixture and stir to smooth out the clumps.
To a bowl, add the drained potatoes, chopped eggs, diced onions, and relish.
Top with the mayonnaise and egg yolk mixture.